Статті в журналах: "Inverse and reverse location theory"

1

Kim, Se-Yun, Hyun-Chul Choi, Jae-Min Lee, and Jung-Woong Ra. "Inverse Scattering Scheme Based on the Moment Method in the Spectral Domain, Part I: Theory." Ultrasonic Imaging 14, no. 1 (January 1992): 16–28. http://dx.doi.org/10.1177/016173469201400102.

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Recently, electromagnetic and ultrasonic imaging of inhomogeneous objects by applying the moment-method procedures of forward scattering problems in the reverse sequence have been developed. In this paper, the inverse scattering formulation has been modified to be applicable in the spectral domain. Compared to previous schemes, the suggested formulation illustrates clearly the actual mechanism of the inverse scattering process by explicit separation of the contributions from several variables, such as the measurement location, basis function, and geometry of objects. The ill-posedness inherent in inverse scattering problems was also explained easily in this spectral scheme by the exponentially-decaying behavior of high-frequency spectral components of the scattered field. It implies that enlargement of the discretized cell size is a key factor in regularizing the ill-posedness. In particular, since the singular kernel to be integrated on each cell became regular in the modified scheme, various types of basis functions instead of pulse function were adopted without additional difficulties. This advantage is expected to play an important role in regularizing the noise effect by selecting polynomial basis function on the enlarged cells of discretization in the spectral inverse scattering scheme.

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2

Zhang, Lei, and Luming Jia. "Near-field imaging for an obstacle above rough surfaces with limited aperture data." Inverse Problems & Imaging 15, no. 5 (2021): 975. http://dx.doi.org/10.3934/ipi.2021024.

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<p style='text-indent:20px;'>This paper is concerned with the scattering and inverse scattering problems for a point source incident wave by an obstacle embedded in a two-layered background medium. It is a nontrivial extension of the previous theoretical work on the inverse obstacle scattering in an unbounded structure [Commun. Comput. Phys., 26 (2019), 1274-1306]. By the potential theory of boundary integral equations, we derive a novel integral equation formula for the scattering problem, then the well-posedness of the system is proved. Based on the singularity analysis of integral kernels, we presented a numerical method for the integral equations. Furthermore, we developed a reverse time migration method for the corresponding composite inverse scattering problem with the limited aperture data. Numerical experiments show that the proposed method is effective to recover the support of an unknown obstacle and the shape, location of the surfaces.</p>

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3

Osipov, Vasiliy, Sergey Kuleshov, Alexandra Zaytseva, and Alexey Aksenov. "Approach for the COVID-19 Epidemic Source Localization in Russia Based on Mathematical Modeling." Informatics and Automation 20, no. 5 (August 13, 2021): 1065–89. http://dx.doi.org/10.15622/20.5.3.

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The paper presents the results of statistical data from open sources on the development of the COVID-19 epidemic processing and a study сarried out to determine the place and time of its beginning in Russia. An overview of the existing models of the processes of the epidemic development and methods for solving direct and inverse problems of its analysis is given. A model for the development of the COVID-19 epidemic via a transport network of nine Russian cities is proposed: Moscow, St. Petersburg, Nizhny Novgorod, Rostov-on-Don, Krasnodar, Yekaterinburg, Novosibirsk, Khabarovsk and Vladivostok. The cities are selected both by geographic location and by the number of population. The model consists of twenty seven differential equations. An algorithm for reverse analysis of the epidemic model has been developed. The initial data for solving the problem were the data on the population, the intensity of process transitions from one state to another, as well as data on the infection rate of the population at given time moments. The paper also provides the results of a detailed analysis of the solution approaches to modeling the development of epidemics by type of model (basic SEIR model, SIRD model, adaptive behavioral model, modified SEIR models), and by country (in Poland, France, Spain, Greece and others) and an overview of the applications that can be solved using epidemic spread modeling. Additional environmental parameters that affect the modeling of the spread of epidemics and can be taken into account to improve the accuracy of the results are considered. Based on the results of the modeling, the most likely source cities of the epidemic beginning in Russia, as well as the moment of its beginning, have been identified. The reliability of the estimates obtained is largely determined by the reliability of the statistics used on the development of COVID-19 and the available data on transportation network, which are in the public domain.

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4

Visnjic, Jelena, Ivana Stanisev, and Yuanyuan Ke. "Reverse order law and forward order law for the (b, c)-inverse." Electronic Journal of Linear Algebra 39 (July 13, 2023): 379–94. http://dx.doi.org/10.13001/ela.2023.7807.

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The reverse order law and the forward order law have been studied for various types of generalized inverses. The $(b,c)$-inverse is a generalization of some well known generalized inverses, such as the Moore-Penrose inverse, the Drazin inverse, the core inverse, etc. In this paper, the reverse order law for the $(b,c)$-inverse, in a unital ring, is investigated and an equivalent condition for this law to hold for the $(b,c)$-inverse is derived. Also, some known results on this topic are generalized. Furthermore, the forward order law for the $(b,c)$-inverse in a ring with a unity is introduced, for different choices of $b$ and $c$. Moreover, as corollaries of obtained results, equivalent conditions for the reverse order law and the forward order law for the inverse along an element are derived.

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5

Castro-Gonzalez, Nieves, and Robert Hartwig. "Perturbation results and the forward order law for the Moore-Penrose inverse of a product." Electronic Journal of Linear Algebra 34 (February 21, 2018): 514–25. http://dx.doi.org/10.13001/1081-3810.3365.

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New expressions are given for the Moore-Penrose inverse of a product $AB$ of two complex matrices. Furthermore, an expression for $(AB)\dg - B\dg A\dg$ for the case where $A$ or $B$ is of full rank is provided. Necessary and sufficient conditions for the forward order law for the Moore-Penrose inverse of a product to hold are established. The perturbation results presented in this paper are applied to characterize some mixed-typed reverse order laws for the Moore-Penrose inverse, as well as the reverse order law.

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6

Zheng, Jie. "The solution of inverse matrix by using unary polynomial ring theory." Highlights in Science, Engineering and Technology 22 (December 7, 2022): 287–92. http://dx.doi.org/10.54097/hset.v22i.3390.

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Matrix is in the core position in algebra, and the inverse matrix is particularly important. So far, there are adjoint matrix method, elementary transformation method, block matrix method and so on in solving the inverse matrix. In this paper, we will introduce a method of seeking the inverse matrix by using unary polynomial ring theory. This method can reverse the matrix equation into the algebra equation, cleverly avoiding the complex matrix equation.

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7

Martin, Benjamin T., Stephan B. Munch, and Andrew M. Hein. "Reverse-engineering ecological theory from data." Proceedings of the Royal Society B: Biological Sciences 285, no. 1878 (May 16, 2018): 20180422. http://dx.doi.org/10.1098/rspb.2018.0422.

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Ecologists have long sought to understand the dynamics of populations and communities by deriving mathematical theory from first principles. Theoretical models often take the form of dynamical equations that comprise the ecological processes (e.g. competition, predation) believed to govern system dynamics. The inverse of this approach—inferring which processes and ecological interactions drive observed dynamics—remains an open problem in ecology. Here, we propose a way to attack this problem using a machine learning method known as symbolic regression, which seeks to discover relationships in time-series data and to express those relationships using dynamical equations. We found that this method could rapidly discover models that explained most of the variance in three classic demographic time series. More importantly, it reverse-engineered the models previously proposed by theoretical ecologists to describe these time series, capturing the core ecological processes these models describe and their functional forms. Our findings suggest a potentially powerful new way to merge theory development and data analysis.

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8

Omidi, Shahede, Jafar Fathali, and Morteza Nazari. "Inverse and reverse balanced facility location problems with variable edge lengths on trees." OPSEARCH 57, no. 2 (December 2, 2019): 261–73. http://dx.doi.org/10.1007/s12597-019-00428-6.

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9

Nazari, Morteza, and Jafar Fathali. "Inverse and Reverse 2-facility Location Problems with Equality Measures on a Network." Iranian Journal of Mathematical Sciences and Informatics 18, no. 1 (April 1, 2023): 211–25. http://dx.doi.org/10.52547/ijmsi.18.1.211.

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10

Qin, Yingying, and Zhiping Xiong. "A Note on the Reverse Order Law for g-Inverse of Operator Product." Axioms 11, no. 5 (May 12, 2022): 226. http://dx.doi.org/10.3390/axioms11050226.

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The generalized inverse has many important applications in aspects of the theoretical research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the reverse order laws for the generalized inverse of the operator product. In this paper, we study the reverse order law for the g-inverse of an operator product T1T2T3 using the technique of matrix form of bounded linear operators. In particular, some necessary and sufficient conditions for the inclusion T3{1}T2{1}T1{1} ⊆ (T1T2T3){1} is presented. Moreover, some finite dimensional results are extended to infinite dimensional settings.

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11

Aranya, Rolee. "Location Theory in Reverse? Location for Global Production in the IT Industry of Bangalore." Environment and Planning A: Economy and Space 40, no. 2 (February 2008): 446–63. http://dx.doi.org/10.1068/a38416.

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This paper is a detailed study of the location history of eight software and information technology (IT) enabled service firms, with varying attributes such as age of firm, type of work undertaken, and ownership sited in the southern Indian city of Bangalore. These cases are used to relate urban restructuring occurring in the city of Bangalore to the strategic shifting of location of firms within the urban fabric. While IT firms cannot be strictly classified as producer services, it is possible to contextualise their location decisions in terms of other office-based economic activities, such as producer services. Findings from the case studies are examined in relation to urban growth theories of the 1980s and 90s, which were related to an expansion of the service sector in advanced economies. The literature discussed in this paper explains the role of growth in producer services in suburbanisation of office space and the development of ‘edge cities’ and ‘suburban downtowns’ as alternatives to and in competition with traditional city centres. Studies of office location and contact patterns indicate the retention of management functions in the CBDs, with a consequent relocation of routine office operations to these suburban office spaces. The findings from the firms studied in Bangalore indicate a reverse pattern of peripheralisation of control functions and a retention of routine production functions in the core urban areas. The limited need for face-to-face contacts with actors in the local urban economy and the export-related output of this offshore industry are contributors to this apparent reversal of location dynamics. The paper briefly concludes with directions for future research on such specialised service production activity that is often being located in cities of developing countries, and its impact on the urban structure of these cities.

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12

Ji, Jun, and Yimin Wei. "The outer generalized inverse of an even-order tensor." Electronic Journal of Linear Algebra 36, no. 36 (September 5, 2020): 599–615. http://dx.doi.org/10.13001/ela.2020.5011.

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Necessary and sufficient conditions for the existence of the outer inverse of a tensor with the Einstein product are studied. This generalized inverse of a tensor unifies several generalized inverses of tensors introduced recently in the literature, including the weighted Moore-Penrose, the Moore-Penrose, and the Drazin inverses. The outer inverse of a tensor is expressed through the matrix unfolding of a tensor and the tensor folding. This expression is used to find a characterization of the outer inverse through group inverses, establish the behavior of outer inverse under a small perturbation, and show the existence of a full rank factorization of a tensor and obtain the expression of the outer inverse using full rank factorization. The tensor reverse rule of the weighted Moore-Penrose and Moore-Penrose inverses is examined and equivalent conditions are also developed.

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13

Niu, Tong, Lin Zhang, Bo Zhang, Bofan Yang, Shengjun Wei, and Paolo Manfredi. "An Improved Prediction Model Combining Inverse Exponential Smoothing and Markov Chain." Mathematical Problems in Engineering 2020 (September 28, 2020): 1–11. http://dx.doi.org/10.1155/2020/6210616.

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On the basis of the triple exponential smoothing prediction model, this paper introduces the reverse prediction idea and establishes the reverse triple exponential smoothing model by setting parameters such as threshold value and iteration times and reasonably correcting its initial value. This method can effectively reduce the error of early prediction value. At the same time, aiming at the problem that the predicting advantage of the reverse triple exponential smoothing model weakens in the later period, Markov theory is introduced to correct its error value, and an improved prediction model combining inverse exponential smoothing and Markov chain is further established. The improved model combines the advantages of index model trend prediction and Markov fluctuation prediction, and the prediction accuracy and stability of the model are significantly improved through case tests.

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14

Mary, X. "Reverse Order Law for the Group Inverse in Semigroups and Rings." Communications in Algebra 43, no. 6 (April 17, 2015): 2492–508. http://dx.doi.org/10.1080/00927872.2014.900562.

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15

He, Longyu. "Design of the Reverse Logistics Network of New Energy Vehicle Waste Power Batteries." E3S Web of Conferences 275 (2021): 02019. http://dx.doi.org/10.1051/e3sconf/202127502019.

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While making an optimistic estimate of the development prospects of new energy vehicles, this article pays attention to the problem of waste power batteries for new energy vehicles. Based on the theory of circular economy, waste batteries reverse logistics location factors and site selection methods, we propose waste power batteries In the design of the reverse logistics network, based on the recycling path of the used power battery reverse logistics network, two recycling modes of the used power battery reverse logistics network are proposed. Based on the location method and recycling mode, a reverse logistics network for the used power battery of new energy vehicles can be constructed.

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16

Sitha, Bibekananda, Jajati Sahoo, and Ratikanta Behera. "Characterization of weighted (b,c) inverse of an element in a ring." Filomat 36, no. 14 (2022): 4629–44. http://dx.doi.org/10.2298/fil2214629s.

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The notion of the weighted (b,c)-inverse of an element in rings were introduced very recently. In this paper, we further elaborate on this theory by establishing a few characterizations of this inverse and their relationships with other (v,w)-weighted (b,c)-inverses. We discuss a few necessary and sufficient conditions for the existence of the hybrid (v,w)-weighted (b,c)-inverse and the annihilator (v,w)-weighted (b, c)-inverse of an element in a ring. In addition, we explore a few sufficient conditions for the reverse-order law of the annihilator (v,w)-weighted (b,c)-inverses.

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17

Kovačić, Danijel, and Marija Bogataj. "Reverse logistics facility location using cyclical model of extended MRP theory." Central European Journal of Operations Research 21, S1 (July 1, 2012): 41–57. http://dx.doi.org/10.1007/s10100-012-0251-x.

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18

Zhang, Guanyu, Yitian Wang, Yiyao Fan, and Chen Chen. "Adaptive Inverse Control Based on Kriging Algorithm and Lyapunov Theory of Crawler Electromechanical System." Complexity 2018 (December 2, 2018): 1–12. http://dx.doi.org/10.1155/2018/1872943.

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The electromechanical system of a crawler is a multi-input, multioutput strongly coupled nonlinear system. In this study, an adaptive inverse control method based on kriging algorithm and Lyapunov theory is proposed to improve control accuracy during adaptive driving. The electromechanical coupling model of the electromechanical system is established on the basis of the dynamic analysis of the crawler. In accordance with the kriging algorithm, the inverse model of the electromechanical system of the crawler is established by offline data. The adaptive travel control law of the crawler is obtained on the basis of Lyapunov theory. Combined with the kriging algorithm, the adaptive driving reverse control method is designed, and the online system is used to update and perfect the inverse system model in real time. Finally, the virtual prototype model of the crawler is established, and the control effect of the adaptive inverse control method is verified by theoretical analysis and virtual prototype simulation.

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19

Hanias, M. P., L. Magafas, and S. G. Stavrinides. "“Reverse Engineering” in Econophysics." International Journal of Productivity Management and Assessment Technologies 7, no. 1 (January 2019): 36–49. http://dx.doi.org/10.4018/ijpmat.2019010103.

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The work presented here is a paradigm of EconoPhysics, i.e. of research in the area of finance and economics by applying physical models, in this case chaos theory. A specific analysis of a macroeconomic model proposed by Vosvrda is presented. The Vosvrda model is an idealized macroeconomic model, combining the savings of households, Gross Domestic Product and the foreign capital inflow. It is simulated by three autonomous differential equations. According to this model, there are six parameters, having their values regulating the system behavior (parameters of Vosvdra). Using artificial noisy data for simulating real data and using an inverse modelling procedure, the authors have fitted and tuned the parameters of Vosvdra differential equations to achieve more accurate solutions. The relevant resultant evaluation showed that the system is a chaotic one, even though for the same values proposed by Vosvrda. Finally, this chaotic behavior has provided the capability to expand the time horizon of the solution, thus achieving reliable forecasting for the system.

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20

Qi, Yang, Liu Xiaoji, and Yu Yaoming. "Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators." Journal of Mathematics 2021 (October 31, 2021): 1–12. http://dx.doi.org/10.1155/2021/6585951.

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In this paper, we study the reverse order law for the Moore–Penrose inverse of the product of three bounded linear operators in Hilbert spaces. We first present some equivalent conditions for the existence of the reverse order law A B C † = C † B † A † . Moreover, several equivalent statements of ℛ A A ∗ A B C = ℛ A B C and ℛ C ∗ C A B C ∗ = ℛ A B C ∗ are also deducted by the theory of operators.

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21

Khonina, Svetlana N., Alexey P. Porfirev, Andrey V. Ustinov, Mikhail S. Kirilenko, and Nikolay L. Kazanskiy. "Tailoring of Inverse Energy Flow Profiles with Vector Lissajous Beams." Photonics 9, no. 2 (February 20, 2022): 121. http://dx.doi.org/10.3390/photonics9020121.

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In recent years, structured laser beams for shaping inverse energy flow regions: regions with a direction of energy flow opposite to the propagation direction of a laser beam, have been actively studied. Unfortunately, many structured laser beams generate inverse energy flow regions with dimensions of the order of the wavelength. Moreover, there are significant limitations to the location of these regions. Here, we investigate the possibility of controlling inverse energy flow distributions by using the generalization of well-known cylindrical vector beams with special polarization symmetry—vector Lissajous beams (VLBs)—defined by two polarization orders (p, q). We derive the conditions for the indices (p, q) in order, not only to shape separate isolated regions with a reverse energy flow, but also regions that are infinitely extended along a certain direction in the focal plane. In addition, we show that the maximum intensity curves of the studied VLBs are useful for predicting the properties of focused beams.

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22

Tjokroaminata, W. D., C. S. Tan, and W. R. Hawthorne. "A Design Study of Radial Inflow Turbines With Splitter Blades in Three-Dimensional Flow." Journal of Turbomachinery 118, no. 2 (April 1, 1996): 353–61. http://dx.doi.org/10.1115/1.2836650.

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An inverse design technique to design turbomachinery blading with splitter blades in three-dimensional flow is developed. It is based on the use of Clebsch transformation, which allows the velocity field to be written as a potential part and a rotational part. It is shown that the rotational part can be expressed in terms of the mean swirl schedule (the circumferential average of the product of radius and tangential velocity) and the blade geometry that includes the main blade as well as the splitter blade. This results in an inverse design approach, in which both the main and the splitter blade geometry are determined from a specification of the swirl schedule. Previous design study of a heavily loaded radial inflow turbine, without splitter blades, for a rather wide variety of specified mean swirl schedules results in a blade shape with unacceptable nonradial blade filament; the resulting reduced static pressure distribution yields an “inviscid reverse flow region” covering almost the first half of the blade pressure surface. When the inverse design technique is applied to the design study of the turbine wheel with splitter blades, the results indicate that the use of splitter blades is an effective means for making the blade filament at an axial location more radial as well as a potential means for eliminating any “inviscid reverse flow” region that may exist on the pressure side of the blades.

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23

Villaverde, Alejandro F., and Julio R. Banga. "Reverse engineering and identification in systems biology: strategies, perspectives and challenges." Journal of The Royal Society Interface 11, no. 91 (February 6, 2014): 20130505. http://dx.doi.org/10.1098/rsif.2013.0505.

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The interplay of mathematical modelling with experiments is one of the central elements in systems biology. The aim of reverse engineering is to infer, analyse and understand, through this interplay, the functional and regulatory mechanisms of biological systems. Reverse engineering is not exclusive of systems biology and has been studied in different areas, such as inverse problem theory, machine learning, nonlinear physics, (bio)chemical kinetics, control theory and optimization, among others. However, it seems that many of these areas have been relatively closed to outsiders. In this contribution, we aim to compare and highlight the different perspectives and contributions from these fields, with emphasis on two key questions: (i) why are reverse engineering problems so hard to solve, and (ii) what methods are available for the particular problems arising from systems biology?

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24

Xue, Xianglian, and Haiyan Jin. "A novel Image Security Protection Method Based on DCT Compression Theory and Hyper-chaotic Mapping." Journal of Physics: Conference Series 2066, no. 1 (November 1, 2021): 012011. http://dx.doi.org/10.1088/1742-6596/2066/1/012011.

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Abstract This paper studies the current situation of image compression encryption and analyzes the influence of low frequency (DC coefficient) and high frequency (AC coefficient) on image structure in DCT transformation. Based on this, a novel image security protection method based on DCT compression theory and hyper-chaotic mapping is proposed. First, the position of the pixel of the original image is disturbed, and converts the image from spatial domain into frequency domain by the two-dimensional DCT transformation and quantization. Second, change the pixel values by modifying the values of the sign bit of AC coefficient and DC coefficient. At last, the encrypted image is obtained by carrying out inverse quantization, inverse transformation and reverse operation by bit.

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25

Zhou, Wanna, Zhiping Xiong, and Yingying Qin. "Forward Order Law for the Reflexive Inner Inverse of Multiple Matrix Products." Axioms 11, no. 3 (March 10, 2022): 123. http://dx.doi.org/10.3390/axioms11030123.

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The generalized inverse has numerous important applications in aspects of the theoretic research of matrices and statistics. One of the core problems of generalized inverse is finding the necessary and sufficient conditions for the reverse (or the forward) order laws for the generalized inverse of matrix products. In this paper, by using the extremal ranks of the generalized Schur complement, some necessary and sufficient conditions are given for the forward order law for A1{1,2}A2{1,2}…An{1,2}⊆(A1A2…An){1,2}.

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26

Antonova, Clemena. "Non-Euclidean Geometry in Russian Art History: On a Little-Known Application of a Scientific Theory." Leonardo 53, no. 3 (May 2020): 293–98. http://dx.doi.org/10.1162/leon_a_01786.

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The author has previously proposed that there are at least six different definitions of “reverse” or “inverse” perspective, i.e. the principle of organizing pictorial space in the icon. Reverse perspective is still a largely unresolved art historical problem. The author focuses on one of the six defi nitions, the one least familiar to Western scholars—namely, the view, common in Russian art-historical writing at the beginning of the twentieth century, that space in the icon is a visual analogue of non-Euclidean geometry. Russian mathematician-turned-theologian and priest Pavel Florensky claimed that the space of the icon is that of non-Euclidean geometry and truer to the way human vision functions. The author considers the scientifi c validity of Florensky's claim.

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27

Guk, N. "FEATURES OF VARIATIONAL FORMULATION OF THE INVERSE PROBLEM OF THE THIN PLATE THEORY." BULLETIN TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV. Mathematics. Mechanics, no. 1(40) (2019): 40–47. http://dx.doi.org/10.17721/1684-1565.2019.01-40.09.40-47.

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The problem of identification of hard inclusions in the material of an elastic plate by the results of strain measurements is considered. The problem is formulated as the inverse problem of the theory of thin plates. The variation formulation contains the functional of the total energy of the plate and an additional condition that determines the proximity of the plate calculated using the mathematical model and the observed states. The search for a solution to the inverse problem is carried out in two stages: the location of the inclusions is determined; the values of the physical and mechanical parameters of the inclusions are specified using the gradient method.

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28

RAMM, A. G. "SOME RESULTS ON INVERSE SCATTERING." Modern Physics Letters B 22, no. 23 (September 10, 2008): 2217–40. http://dx.doi.org/10.1142/s0217984908016996.

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A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: (1) Property C and applications, (2) Stable inversion of fixed-energy 3D scattering data and its error estimate, (3) Inverse scattering with “incomplete” data, (4) Inverse scattering for inhomogeneous Schrödinger equation, (5) Krein's inverse scattering method, (6) Invertibility of the steps in Gel'fand–Levitan, Marchenko, and Krein inversion methods, (7) The Newton–Sabatier and Cox–Thompson procedures are not inversion methods, (8) Resonances: existence, location, perturbation theory, 9) Born inversion as an ill-posed problem, (10) Inverse obstacle scattering with fixed-frequency data, (11) Inverse scattering with data at a fixed energy and a fixed incident direction, (12) Creating materials with a desired refraction coefficient and wave-focusing properties.

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29

Whiteley, Jonathan P. "The Solution of Inverse Non-Linear Elasticity Problems That Arise When Locating Breast Tumours." Journal of Theoretical Medicine 6, no. 3 (2005): 143–49. http://dx.doi.org/10.1080/10273660500148606.

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Non-linear elasticity theory may be used to calculate the coordinates of a deformed body when the coordinates of the undeformed, stress-free body are known. In some situations, such as one of the steps in the location of tumours in a breast, the coordinates of the deformed body are known and the coordinates of the undeformed body are to be calculated, i.e. we require the solution of the inverse problem. Other than for situations where classical linear elasticity theory may be applied, the simple approach for solving the inverse problem of reversing the direction of gravity and modelling the deformed body as an undeformed body does not give the correct solution. In this study, we derive equations that may be used to solve inverse problems. The solution of these equations may be used for a wide range of inverse problems in non-linear elasticity.

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30

Burnete, Sorin. "On The East-West Trade in Skill Intensive Tasks: Theory vs. Evidence." Human and Social Studies 6, no. 1 (March 1, 2017): 34–51. http://dx.doi.org/10.1515/hssr-2017-0003.

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Abstract In keeping with an already entrenched paradigm, international trade in tasks exerts upward pressure upon skilled workers’ wages in both home and host countries. Yet certain empirical evidence from intra-European trade shows that sometimes things occur in reverse, that is high skilled workers’ wages in home countries may decline as a result of offshoring, an outcome that looks like an inverse “maquiladora effect”. I try to show that such deviations do not fly in the face of mainstream theory but rather, they reflect the different conditions under which offshoring is performed today as compared to the ones prevailing two decades ago.

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Richards, R. F., B. N. Munk, and O. A. Plumb. "Fire detection, location and heat release rate through inverse problem solution. Part I: Theory." Fire Safety Journal 28, no. 4 (June 1997): 323–50. http://dx.doi.org/10.1016/s0379-7112(97)00005-2.

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32

Hidan, Muajebah, Mohamed Akel, Salah Mahmoud Boulaaras, and Mohamed Abdalla. "On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions." Journal of Function Spaces 2021 (April 30, 2021): 1–10. http://dx.doi.org/10.1155/2021/9967855.

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Recently, the applications and importance of integral transforms (or operators) with special functions and polynomials have received more attention in various fields like fractional analysis, survival analysis, physics, statistics, and engendering. In this article, we aim to introduce a number of Laplace and inverse Laplace integral transforms of functions involving the generalized and reverse generalized Bessel matrix polynomials. In addition, the current outcomes are yielded to more outcomes in the modern theory of integral transforms.

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33

Lovrić, Milivoj, and Šebojka Komorsky-Lovrić. "Theory of reverse scan square-wave voltammetry influenced by the kinetics of reactant adsorption." Open Chemistry 8, no. 3 (June 1, 2010): 513–18. http://dx.doi.org/10.2478/s11532-010-0034-y.

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AbstractA model of electrode reaction complicated by slow adsorption of the reactant is developed for square-wave voltammetry with inverse scan direction. The relationship between the dimensionless net peak current and the logarithm of dimensionless rate constant of adsorption is a curve with a minimum and a maximum. For this reason the ratio of real net peak current and the square-root of frequency is a non-linear function of the logarithm of frequency and exhibits either a maximum or a minimum. The frequency of extreme serves for the estimation of the rate constant: log(k ads /D 1/2 ) = log(k*ads )crit + 0.5 log f crit , where (k*ads )crit is a critical dimensionless rate constant of adsorption. Square-wave voltammetry is sensitive to the kinetics of adsorption if k ads 2 cm s−1

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34

Lu, Xiao Yang, Bing Tao Tang, and Xiao Li Lu. "New Characteristics of Inverse Analysis Method and its Application in Sheet Metal Formability Prediction." Advanced Materials Research 102-104 (March 2010): 257–61. http://dx.doi.org/10.4028/www.scientific.net/amr.102-104.257.

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Information of initial flat blank and final workpiece is prerequisite and satisfactory blank configuration and thickness distribution can be obtained, which is very important at the preliminary design stage. The theory and improvements of inverse analysis method of sheet metal forming based on deformation theory of plasticity is explored. In order to take into account the bending effects, this approach with CST membrane element and DKT6 plate bending element superposed to obtain the DKT12 shell element is fully introduced. An ideal reverse deformation method is implemented to improve the initial solution obtained by radical length development method. Application to a square box deep drawing case is presented with emphasis on the efficiency and usefulness of the proposed improved methods.

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35

Synkevych, R. O. "Methods and information systems for identification of sources of radioactive air pollution by inverse modeling." Mathematical machines and systems 4 (2021): 78–90. http://dx.doi.org/10.34121/1028-9763-2021-4-78-90.

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The paper reviews the methods for identifying an unknown source of pollution by inverse mod-eling and information systems for air pollution forecasting and analysis. Several different for-eign and Ukrainian air pollution forecasting systems, such as the European Union's Nuclear Emergency Response System RODOS, have been developed on the basis of atmospheric transport models. However, the key data that determine the quality of forecasting in such sys-tems are the characteristics of the emission sources. In the case of detection of pollution from an unknown emission source, there should be performed inverse simulation. The use of the RODOS system, as well as other existing forecasting systems for such a task is possible but it requires multiple manual start of calculations of atmospheric transfer models in the reverse mode. Presented in the paper results of the application of inverse modeling methods during ra-diation incidents of the last decade demonstrate that modern methods of inverse modeling are sufficiently developed to set the task of automating inverse modeling in information systems for air pollution analysis and forecasting. Even though these methods not always can exactly identify the source of emissions due to the lack of measurements and poor conditioning of the inverse atmospheric transport problem, their application always leads to a significant reduction (by an order of magnitude or more) in the search for unknown sources compared to the detec-tion of pollutants. At present, in the existing forecasting systems the methods of inverse model-ing are only partially automated, namely for the case of known location and unknown emissions of the source of pollution. Therefore, this paper proposes the architecture of the future system for identifying unknown sources of emissions by inverse modeling.

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36

Fang, Jinwei, Hui Zhou, Hanming Chen, Ning Wang, Yufeng Wang, Pengyuan Sun, and Jianlei Zhang. "Source-independent elastic least-squares reverse time migration." GEOPHYSICS 84, no. 1 (January 1, 2019): S1—S16. http://dx.doi.org/10.1190/geo2017-0847.1.

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Elastic least-squares reverse time migration (LSRTM) has been developed recently for its high accuracy imaging ability. The theory is based on minimizing the misfit between the observed and simulated data by an iterative algorithm to refine seismic images toward the true reflectivity. We have developed a new elastic LSRTM with the same modeling equations for source and receiver wavefield extrapolations, except for their source terms. The LSRTM has a natural advantage to solve the source and receiver wavefields using the same modeling system; thus, it is easy to implement LSRTM. In practice, it is difficult to obtain an accurate source wavelet, so a convolution-based objective function is used in our source-independent elastic LSRTM. Such an objective function can relax the requirement of an accurate wavelet, and improve the robustness of the inverse problem in the presence of noise. The numerical examples indicate that our method has the ability to recover the reflectivity models with an incorrect source wavelet from noisy data.

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37

Yu, Jianhua, and Gerard T. Schuster. "Crosscorrelogram migration of inverse vertical seismic profile data." GEOPHYSICS 71, no. 1 (January 2006): S1—S11. http://dx.doi.org/10.1190/1.2159056.

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We present the theory of crosscorrelogram migration of ghost reflections, also known as interferometric imaging, to delineate reflector geometries from inverse vertical seismic profile data. The theory includes the equations for forward modeling, migration, asymptotic inversion, and model resolution of crosscorrelgrams. Rather than using primary reflections, crosscorrelogram migration can use ghost reflections to reconstruct the reflector geometry. Other multiples can be used as well, including pegleg multiples and higher-order multiples. Its main advantages over conventional Kirchhoff migration are (1) both source location (e.g., drill-bit position) and source wavelet need not be known (such as when using a drill bit as a source in a deviated well), (2) it is insensitive to source-related static errors, and (3) it has wider subsurface illumination than conventional Kirchhoff migration of primary reflections. Crosscorrelation migration can effectively widen the source-receiver aperture by more than 50% compared to standard inverse vertical seismic profile (IVSP) migration. The primary disadvantages are (1) it uses ghost reflections for imaging, which can be weaker (or sometimes more distorted) than primary reflections; (2) crosscorrelation creates virtual multiples that can sometimes appear as coherent noise in the final image; and (3) it has poorer horizontal resolution than standard IVSP migration. Results from imaging simulated IVSP traces show that crosscorrelation migration produces reflectivity-like images that correlate well with the actual reflector geometry of a layered fault model. These images are almost completely immune to static errors at the source location and have wider subsurface illumination than conventional IVSP migration images. We also apply crosscorrelation migration to IVSP data recorded at a Friendswood, Texas, test site. Results show that the crosscorrelation image correlates better with the well log and wider subsurface illumination than a conventional Kirchhoff migration image.

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38

Tao, Ke, and Xing Liu. "Motion Analysis and Research on Mobile Swing Type Manipulator." Advanced Materials Research 588-589 (November 2012): 194–97. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.194.

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The working space and the end-effector pose of the two degrees of freedom mobile swing type manipulator are analyzed, through homogeneous coordinate transformation to establish the transformation relationship between operating space coordinate and each joint space coordinate, derived the end-effector pose matrix , using the inverse transformation method to seek motion reverse solution. Application of linear interpolation theory, doing trajectory planning for arbitrary movement path, show manipulator in its working space can realize arbitrary trajectory.

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39

Ahn, John, Christine Alar, Beth Bjorkman, Steve Butler, Joshua Carlson, Audrey Goodnight, Haley Knox, Casandra Monroe, and Michael C. Wigal. "Ordered multiplicity inverse eigenvalue problem for graphs on six vertices." Electronic Journal of Linear Algebra 37 (May 10, 2021): 316–58. http://dx.doi.org/10.13001/ela.2021.5005.

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For a graph $G$, we associate a family of real symmetric matrices, $\mathcal{S}(G)$, where for any $M \in \mathcal{S}(G)$, the location of the nonzero off-diagonal entries of $M$ is governed by the adjacency structure of $G$. The ordered multiplicity Inverse Eigenvalue Problem of a Graph (IEPG) is concerned with finding all attainable ordered lists of eigenvalue multiplicities for matrices in $\mathcal{S}(G)$. For connected graphs of order six, we offer significant progress on the IEPG, as well as a complete solution to the ordered multiplicity IEPG. We also show that while $K_{m,n}$ with $\min(m,n)\ge 3$ attains a particular ordered multiplicity list, it cannot do so with arbitrary spectrum.

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40

Shevchenko, O. "Reverse Task of Heat Conductivity for the Semilimited Bar." Metrology and instruments, no. 5 (October 24, 2019): 27–31. http://dx.doi.org/10.33955/2307-2180(5)2019.27-31.

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The article concerns methods and formulas for the calculation of the coefficient of thermal conductivity of solid bodies using the known solutions of direct thermal conductivity tasks. The solution to the inverse problem of heat conductivity is based on the quite complicated methods including both hyperbolic functions and finite-difference methods. Under certain experimental conditions, the task is simplified at the regular thermal modes of 1, 2, or 3 types. Thus final formulas are simplified to algebraic equations. The simplification of the inverse problem of heat conductivity to algebraic equations is possible using other approaches. These methods are based on the analysis of the reference points, zero values of temperature distribution function, function inflection points, and its first and second derivatives. Here, we present formulas for the calculations of the temperature field on the assumption of the direct task solution for the half-bounded bar under the pulsed heating followed the re-definition of the boundary conditions. The article describes two methods in which solutions are reduced to simple algebraic formulas when using the specified points on heating thermograms of test examples. These solutions allow algebraic deriving of simple relations for inverse problems of determination of thermophysical characteristics of solid bodies. The calculation formulas are given for the determination of the heat conductivity coefficient determination by two methods: by value of temperature, coordinate, and two moments at which this temperature is reached. The second method uses the values of two coordinates of the test sample in two different points where the equal temperature is reached at different points in time. The final solution of the equation is logarithmic. The analysis of known methods and techniques shows that experimental methods are oriented on the technical implementation and based on facilities of available equipment and instruments. Existing experimental techniques are based on specific constructions of measuring facilities. Simultaneously, there are well-studied methods of solution of thermal conductivity standard tasks set out in fundamental issues. The theoretical methods come from axioms, equations, and theoretical postulates, and they give the solution of inverse tasks of thermal conductivity. This work uses the solutions of direct tasks presented in the monograph by A.V.Lykov “The theory of heat conductivity”. These solutions have a good theoretical background and experts’ credit. The boundary conditions of the problem are next: the half-bounded thin bar is given. The side surface of the bar has a thermal insulation. At the initial moment, the instant heat source acts on the bar in its section at some distance from its end. Heat exchange occurs between the environment and the end of the bar according to Newton’s law. The initial (relative) temperature of the bar is accepted equal to zero. The heat exchange between the free end face of the bar and the environment is gone according to Newton’s law.

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41

Trung, Nguyen Dinh, Dinh Tran Ngoc Huy, Paitoon Chetthamrongchai, Karrar Shareef Mohsen, Ahmad Syarief Iskandar, A. Nurjaya, Denok Sunarsi, Krishanveer Singh, and Supat Chupradit. "Optimizing the Interaction Between Two Closed-Loop Supply Chains Based on Inverse Logistics Using the Game Theory Method." Foundations of Computing and Decision Sciences 47, no. 4 (December 1, 2022): 455–67. http://dx.doi.org/10.2478/fcds-2022-0025.

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Abstract Over the past few years, attention to environmental problems, legal necessities, and economic advantages emerging from reproduction activities has attracted attention to reverse logistics activities in the form of a closed-loop supply chain, whether in industry or scientific research. The current study aims to model competitiveness and comparison between two closed-loop three-level supply chains, each of which includes a manufacturer, a retailer, and a third party to collect the products used by the customer, taking into account the concepts of game theory and the existence of aggregates. Moreover, a separate supplier for each chain is considered. In the forward supply chain, the manufacturer produces new products using new components or re-used products that have been collected from the consumer, then sells these products mainly to the retailer, and the retailer sells them. In the reverse chain, the collector provides the used products to the manufacturer after collection. The study utilized the definitions and concepts of game theory to model this closed loop chain as a Stackelberg game to obtain the optimal value of wholesale and retail price and the optimal value of the product return coefficient for the collector. Finally, the models based on some numerical examples are solved. Given the results, the remanufacturing costs have a significant role in making more profits for all members in such chains, and competitive chains should attempt to remanufacture the products at lower costs.

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42

Majchrzak, Ewa, and Jerzy Mendakiewicz. "Sensitivity Analysis as a Tool of Optimal Sensors Location for Solidification Parameters Estimation." Materials Science Forum 638-642 (January 2010): 2640–45. http://dx.doi.org/10.4028/www.scientific.net/msf.638-642.2640.

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The paper deals with the inverse problems appearing in the thermal theory of foundry processes. In particular, the problems connected with identification of casting and mould thermophysical parameters can be considered. To estimate the parameters determining heat transfer processes in the system casting-mould, the additional information concerning the changes of temperature at the points selected from the domain considered is necessary. The localization of sensors should assure the best conditions of identification process. Generally speaking, the sensor should be located at the point for which the sensitivity of temperature field with respect to parameter estimated achieves maximum. In the case of simultaneous identification of several parameters, the proper choice of sensors localization is more complicated. The main goal of the paper is to discuss a theoretical base connected with the problem formulated, to present the possibilities of numerical methods application, to solve the problem, and finally to show the examples of inverse problems solutions (in particular, the latent heat of binary alloy will be estimated).

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43

Pourmostaghimi, Vahid, Farshad Heidari, Saman Khalilpourazary, and Mohammad Reza Chalak Qazani. "Application of Evolutionary Optimization Techniques in Reverse Engineering of Helical Gears: An Applied Study." Axioms 12, no. 3 (March 1, 2023): 252. http://dx.doi.org/10.3390/axioms12030252.

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Reverse engineering plays an important role in the manufacturing and automobile industries in designing complicated spare parts, reducing actual production time, and allowing for multiple redesign possibilities, including shape alterations, different materials, and changes to other significant parameters of the component. Using reverse engineering methodology, damaged gears can be identified and modeled meticulously. Influential parameters can be obtained in the shortest time. Because most of the time it is impossible to solve gear-related inverse equations mathematically, metaheuristic methods can be used to reverse-engineer gears. This paper presents a methodology based on measurement over balls and span measurement along with evolutionary optimization techniques to determine the geometry of a pure involute of a cylindrical helical gear. Advanced optimization techniques, i.e., Grey Wolf Optimization, Whale Optimization, Particle Swarm Optimization, and Genetic Algorithm, were applied for the considered reverse engineering case, and the effectiveness and accuracy of the proposed algorithms were compared. Confirmatory calculations and experiments reveal the remarkable efficiency of Grey Wolf Optimization and Particle Swarm Optimization techniques in the reverse engineering of helical gears compared to other techniques and in obtaining influential gear design parameters.

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44

Mao, Weijian, and Graham W. Stuart. "Transmission‐reflection tomography: Application to reverse VSP data." GEOPHYSICS 62, no. 3 (May 1997): 884–94. http://dx.doi.org/10.1190/1.1444196.

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A multiphase tomographic algorithm is presented that allows 2-D and 3-D slowness (inverse of velocity) and variable reflector depth to be reconstructed simultaneously from both transmission and reflection traveltimes. We analyze the ambiguity in the determination of velocity and depth in transmission and reflection data and realize that depth perturbation is more sensitive to reflection traveltime anomalies than slowness perturbation, whereas the reverse is true of transmission traveltime anomalies. Because of the constraints on velocity and depth provided by the different wave types, this algorithm reduces the ambiguity substantially between velocity and depth prevalent in reflection tomography and also avoids the undetermined problem in transmission tomography. The linearized inversion was undertaken iteratively by decoupling velocity parameters from reflector depths. A rapid 2-D and 3-D ray‐tracing algorithm is used to compute transmission and reflection traveltimes and partial derivatives with respect to slowness and reflector depth. Both depth and velocity are parameterized in terms of cubic B‐spline functions. Synthetic examples indicate the improvement in tomographic results when both transmission and reflection times are included. The method has been applied to a reverse vertical seismic profile (VSP) data set recorded on the British coal measures along a crossed‐linear array. Traveltimes were picked automatically by the simultaneous determination of time delays and stacking weights using a waveform matching technique. The tomographic inversion of the observed reverse VSP images two fault‐zones of lower velocity than the surrounding media. The location of the faults was confirmed by near‐by reflection lines. The technique can be applied to offset VSPs or reverse VSPs and coincident VSP and surface reflection data.

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45

He, Xue Ming, Jun Fei He, Mei Ping Wu, Rong Zhang, and Xiao Gang Ji. "Reverse Engineering of Free-Form Surface Based on the Closed-Loop Theory." Scientific World Journal 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/903624.

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To seek better methods of measurement and more accurate model of reconstruction in the field of reverse engineering has been the focus of researchers. Based on this, a new method of adaptive measurement, real-time reconstruction, and online evaluation of free-form surface was presented in this paper. The coordinates and vectors of the prediction points are calculated according to a Bézier curve which is fitted by measured points. Final measured point cloud distribution is in agreement with the geometric characteristics of the free-form surfaces. Fitting the point cloud to a surface model by the nonuniform B-spline method, extracting some check points from the surface models based on grids and a feature on the surface, review the location of these check points on the surface with CMM and evaluate the model, and then update the surface model to meet the accuracy. Integrated measurement, reconstruction, and evaluation, with the closed-loop reverse process, established an accurate model. The results of example show that the measuring points are distributed over the surface according to curvature, and the reconstruction model can be completely expressed with micron level. Meanwhile, measurement, reconstruction and evaluation are integrated in forms of closed-loop reverse system.

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46

Li, Han, Wenshu Xie, Meilin Wen, Shufu Li, Yi Yang, and Linhan Guo. "An Optimal Location-Allocation Model for Equipment Supporting System Based on Uncertainty Theory." Symmetry 15, no. 2 (January 25, 2023): 338. http://dx.doi.org/10.3390/sym15020338.

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Scientific support depot location and reasonable spare parts transportation are the keys to improving the support level of complex systems. The current equipment support system has the problems of chaotic warehouse layout and low efficiency of spare parts. The reliability and completeness of spare parts’ historical data are hard to believe. In order to deal with the cognitive uncertainty caused by the asymmetry of data, this paper adopts the uncertainty theory to optimize the depot location and transportation volume. Under the constraints of shortage rate, supply availability, average logistic delay time, and inventory limit, the uncertain chance-constrained model of equipment supporting depot is established. The optimization model is transformed into a deterministic model by using the inverse uncertainty distribution. The genetic algorithm is used to optimize the solution of this model. Finally, the practicability and operability of the model method are verified through the example analysis.

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47

Yen, Ching-Shih, and Enboa Wu. "On the Inverse Problem of Rectangular Plates Subjected to Elastic Impact, Part I: Method Development and Numerical Verification." Journal of Applied Mechanics 62, no. 3 (September 1, 1995): 692–98. http://dx.doi.org/10.1115/1.2896002.

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A method to identify both the impact location and the transverse impact force history from the strain responses at certain points on a rectangular plate is presented. The governing equations of the plate were obtained by applying the Reissner-Mindlin plate theory and the Rayleigh-Ritz method. The strain response was related to the impact force by solving the above equations using the eigenmode expansion method. A mutuality relationship among any pairs of strain responses was used to find the impact location without knowing in advance the impact force history. The force history was subsequently determined after the impact location was identified. The conjugate gradient method was adopted to search for the optimal impact location as well as the force history. Numerical verification was performed using randomly generated impact locations and force histories to simulate impact events. The excellent agreement showed the effectiveness and the validity of the proposed method.

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48

Bomba, A., and A. Safonyk. "Identification of mass-transfer coefficient in spatial problem of filtration." Mathematical Modeling and Computing 1, no. 2 (2014): 135–43. http://dx.doi.org/10.23939/mmc2014.02.135.

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A modeling problem of the process of liquid multi component decontamination by a spatial filter is considered, it takes into account the reverse influence of decisive factors (contamination concentrations of liquid and sediment) on characteristics (coefficient of porosity, diffusion) of the medium and gives us the possibility to determine small mass transfer coefficient under the conditions of prevailing of convective constituents over diffusive ones. An algorithm of the solution of the corresponding nonlinear singular disturbed inverse problem of "convection-diffusion mass transfer" type is suggested.

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49

Dutta, Gaurav, Matteo Giboli, Cyril Agut, Paul Williamson, and Gerard T. Schuster. "Least-squares reverse time migration with local Radon-based preconditioning." GEOPHYSICS 82, no. 2 (March 1, 2017): S75—S84. http://dx.doi.org/10.1190/geo2016-0117.1.

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Least-squares migration (LSM) can produce images with better balanced amplitudes and fewer artifacts than standard migration. The conventional objective function used for LSM minimizes the L2-norm of the data residual between the predicted and the observed data. However, for field-data applications in which the recorded data are noisy and undersampled, the conventional formulation of LSM fails to provide the desired uplift in the quality of the inverted image. We have developed a least-squares reverse time migration (LSRTM) method using local Radon-based preconditioning to overcome the low signal-to-noise ratio (S/N) problem of noisy or severely undersampled data. A high-resolution local Radon transform of the reflectivity is used, and sparseness constraints are imposed on the inverted reflectivity in the local Radon domain. The sparseness constraint is that the inverted reflectivity is sparse in the Radon domain and each location of the subsurface is represented by a limited number of geologic dips. The forward and the inverse mapping of the reflectivity to the local Radon domain and vice versa is done through 3D Fourier-based discrete Radon transform operators. The weights for the preconditioning are chosen to be varying locally based on the relative amplitudes of the local dips or assigned using quantile measures. Numerical tests on synthetic and field data validate the effectiveness of our approach in producing images with good S/N and fewer aliasing artifacts when compared with standard RTM or standard LSRTM.

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50

Tan, Li Guang, Xiao Ting Xiao, Hua Dian Wen, and Qiao Yu Chen. "Study on Deep Drawing Law of the Cylindrical Part with Prefabricate-Holes Based on Inverse Finite Element Method and Forward Finite Element Method." Applied Mechanics and Materials 170-173 (May 2012): 3086–90. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.3086.

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According to processing characteristics of getting rectangular holes after forming of the cylindrical part with prefabricate-holes, the optimum blank shape of the cylindrical part is necessary to improve product quality and reduce production cost. Theory analysis and numerical simulations combined with inverse finite element method and forward finite element method by using ETA/ DYANFORM were employed to investigate the influence on blank shape by the holes, modify the reverse blank shape and optimize the deep drawing by forward simulation,and finally obtain the forming law of the cylindrical part with prefabricate-holes.

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